Abstract
The relationship between the approximateLie-Backlund symmetries and the approximate conservedforms of a perturbed equation is studied. It is shownthat a hierarchy of identities exists by which thecomponents of the approximate conserved vector or theassociated approximate Lie-Backlund symmetries aredetermined by recursive formulas. The results areapplied to certain classes of linear and nonlinear waveequations as well as a perturbed Korteweg-de Vriesequation. We construct approximate conservation laws forthese equations without regard to aLagrangian.
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Kara, A.H., Mahomed, F.M. & Unal, G. Approximate Symmetries and Conservation Laws with Applications. International Journal of Theoretical Physics 38, 2389–2399 (1999). https://doi.org/10.1023/A:1026684004127
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DOI: https://doi.org/10.1023/A:1026684004127